Blender on Second Monitor suddenly lags
I still don't know the answer to the overall issue, but I have found why this occurred for me specifically.

First, turning off Windows Aero (or doing anything that disables it) will solve this problem. With Aero on, it seems that I get normal performance on 2 of the 3 monitors. In the past, my web browsing monitor was the odd man out. After some flipping things around, I found that whichever monitor was plugged in second (out of 3) will be the one that has issues. So un plugging and re-plugging the screen I wanted good performance on solved the problem, even with Aero enabled.

There must be a lot of variables going on behind the scene that I don't understand, so if anyone ever figures that out I'll be happy to pick a new answer. But for now, this does shed some light on the situation.